Theoretical/Computational Chemistry (as well as Physics) plays an important role in the rapid development of modern technologies such as nanotechnology and biotechnology. So far it has provided a nice explanation to the origin of many experimental results. Moreover, theoretical works can suggest possible candidates for future functional materials based on theoretical foundations. Many methods have been developed in theoretical/computational chemistry, but most of them focus on the static (or ground state) properties of materials such as a binding energy, a ground state electronic density, and so on. They just fix the nuclear position, and then they calculate the ground state energy and electronic density. Even if nuclei move, they consider the nuclei just movig on the ground state surface. The basic idea here is that nuclei move much slower than electrons. Then, nuclei move along the potential generated by the fast moving electrons as they are uncorrelated. These methods are very limited to more dynamial processes like a chemical reaction with an extra energy and the light-matter interaction because the electron-nuclear correlation plays a major role. Such cases are called as excited state phenomena which are actually ubiquitous in nature like vision process and photosynthesis. In our group, we are interested in the theoretical/computational description of excited state phenomena and its applications with following questions:

(1) How can we describe correlated electron-nuclear motions correctly?

(2) How can we deal with chemical reactions in the excited states?

(3) Based on our knowledge, how can we design functional molecular devices such as energy materials, nano-electronic/photonic devices?

Research Interests

Development of an algorithm for excited state molecular dynamics

Description of chemical reactions with conical intersections

Design for multi-functional devices

Development of a novel algorithm for excited state molecular dynamics

Born-Oppenheimer (BO) approximation has been a fundamental basis for understanding chemical reactions. Due to the large mass-ratio between electrons and nuclei, one can visualize a chemical reaction as a moving nuclei on a certain potential energy surface (PES), the so-called BOPES or adiabatic PES, generated by the fast electronic motion. For a chemical reaction without any external perturbation such as a laser, this BO approximation works well since the system tends to be bound in a local minima of the ground state potential energy surface. However, when we shine a light on a molecule, the molecule may absorb an energy, an "excitation energy", from the light and transit to a specific state, an "excited state". In this case, something interesting can happen due to electron-nuclear correlation. The molecule can travel around a nuclear configurational space, and it can touch a weird region, the so-called "non-adiabatic" coupling region, where the electron-nuclear correlation is important. Then, suddenly, the moving nuclei behave like quantum particles, i.e. a nuclear density splits into more than two piecies in a nuclear configuration space, thus BO approximation breaks down.

To explain the excited state phenomena, many theoretical/computational methods have been developed so far. Most of them are based on Born-Huang (BH) expansion which uses multiple BOPESs and BO electronic states with non-adiabatic coupling between them. The exact quantum description with BH expansion can give a very nice explanation for excited state dynamics, but the exact calculation is suitable only for small degrees of freedoms. (Here, the "exact" calculation means ab initio calculation without any parameteres.) For a practical application, we need an approximation. The most appropriate candidate is a mixed quantum-classical (MQC) description for molecular system, i.e. we treat the nuclear motion classically and electronic motion quantum mechanically. Then, the most important thing here is to obtain "the force" for classical nuclei. How can we obtain the classical force when nuclei are in the middle of a non-adiabatic process? Is it from one of the BOPESs (surface hopping-type) or from a mixed surface (Ehrenfest-type)?

To answer this question, we exploit a completely new concept, namely the exact factorization scheme. The details of the exact factorization can be found in the series of papers[1-5]. The main point is that we make a "single" product of a conditional electronic wave function and a nuclear wave function (with a partial normalization condition). Then, we can obtain coupled equations for electrons and nuclei including the "full" electron-nuclear correlation. Interestingly, the nuclei move on a "single" potential energy surface (with a Berry-type vector potential), so that we can obtain the classical force from an appropriate classical approximations. In our group, we develop a novel algorithm for the excited state phenomena based on the above exact factorization scheme[6].

Description of chemical reactions with conical intersections

A conical intersection (CI) is one of the most important topics in excited state phenomena. The CI is known to be related with very interesting properties such as a molecular Berry phase, ultrafast nuclear configurational changes, and radiationless decays. Despite of its interesting behaviors, the theoretical description of CI is extremely difficult since we have to know the positions of CIs in the nuclear configurational space. However, the concept of CI is defined in terms of BOPESs, the adiabatic surfaces. When we deal with CIs based on the exact factorization which is mentioned in the previous section, something interesting may arise. First of all, it is shown that one type of CIs (as well as the corresponding molecular Berry phase) does not appear if we deal with the "whole" molecular system exactly, i.e. if we treat the nuclear degrees of freedom quantum mechanically as well [5]. It is reported that many approximated methods have failed to reproduce the exact quantum dynamics in the presence of CIs. The important example is pyrazine. Here, in our group, we target to describe the correct quantum result with our method based on the exact factorization.